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%matplotlib inline

Lotka-Volterra model implemented in FABM

The equations read:

$$ \begin{aligned} \dot{x} &= \alpha x - \beta x y \\ \dot{y} &= \delta x y - \gamma y \end{aligned} $$

where $x$ represents prey and $y$ represents predator. $ \alpha, \beta, \delta$ and $\gamma$ are model parameters defining the interactions between the spicies.

For further information see.

The implementation of the Lotka-Volterra equations in FABM was done by Fenjuan Hu when she started her PhD to get familiar with the FABM framework.

Import standard python packages



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import numpy
import scipy.integrate

Import pyfabm - the python module that contains the Fortran based FABM



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import pyfabm
#pyfabm.get_version()

Configuration

The model configuration is done via the YAML formatted file.

We configure two instances of the Lotka-Volterra model - named LV1 and LV2.

FABM allows for any number of model instances.



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yaml_file = '../../../../testcases/fabm-au-prey_predator.yaml'
model = pyfabm.Model(yaml_file)
model.findDependency('bottom_depth').value = 1.
model.checkReady(stop=True)
y0 = model.state

Model increment



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def dy(y,t0):
    model.state[:] = y
    return model.getRates()

Time axis and model integration



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t = numpy.linspace(0,200.,100)
y = scipy.integrate.odeint(dy,model.state,10000*t)

Plot the results



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import pylab
pylab.plot(t,y)
pylab.title('Time series plots')
pylab.legend([variable.path for variable in model.state_variables])
pylab.show()

pylab.plot(y[:,0],y[:,1])
pylab.plot(y[:,2],y[:,3])
pylab.title('Limit circles')
pylab.show()

The Lotka-Volterra equations in a different context:

https://www.youtube.com/watch?v=MjPFHWul2J0&t=6m1s



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